I don’t understand when a ship may sail. Does she sail only when she’s full (6 sailors and 6 merchants), or must she sail when at least one sailor is on board, or have the players the choice? In the last case, which player? The captain only?

Hopefully someone more knowledgeable than me will come along and answer this question, but as I read the rules, it seems that any ship with at least one sailor on it sails during Phase 4. The captain could choose to sail a tiny amount and stop I suppose, but I think that the ship does at least leave the home port in Phase 4 if it has any sailors.

The answer depends on whether you are playing the basic or advanced version, and upon a one-sentence difference in the corrected Phase 4 rules for the two versions.

The Phase 4 basic rules say that the ships "sail one after the other." There is no other mention of time, so this means a ship must sail, unless it has just been refitted in the immediately preceding Phase 3 (in the basic game, ships must wait one turn after refitting). The mandatory sailing is possible because in the basic game the four ships are always fully crewed during refit, per the rules for Phase 3.

The Phase 4 advanced rules add the following sentence, which is critical: "Ships fitted out during phase 3 may sail immediately." The key word is "may". This means a ship does not have to sail. This makes sense because in the advanced game ships are crewed (or not) via the players' choices in Phase 3, rather than being fully crewed automatically as in the basic game. Note also that the same sentence says that ships may sail immediately. In other words, ships do not have to wait for a turn after refitting as they do in the basic game. Since the rules say that "Ships are controlled by their skipper", in the advanced game the player with the left-most sailor on a ship makes the decision whether or not that ship will sail.